W

 

   

 

 St

Ex

 Ch

Hy

Ya 

 

 

 

 

 

 

 

 

 

 

Copy

PHB

repr

 

orking 

ticky

xpla

hang Yo

yun Joo

 Kang 

yright © 2016

S working pa

oduction for 

Paper 

y Div

anat

ong Ha 

ong Im 

6 by Chang Yo

pers are distr

other purpos

No. 20

vide

ion 

 

ong Ha, Hyun

ributed for di

ses requires t

016006

ends

n Joong Im an

iscussion and

the consent o

s: A N

nd Ya Kang an

d comment p

of the copyrig

New

nd. All rights r

urposes only.

ght holder. 

w 

reserved. 

. Any additionnal   

Sticky dividends: A new explanationI

Chang Yong Haa, Hyun Joong Ima,∗, Ya Kangb

aHSBC Business School, Peking University, University Town, Nanshan District, Shenzhen,518055, China

bNUS Business School, National University of Singapore, BIZ 2 Building #B1-3, 1 Business Link,117592, Singapore

Abstract

This study proposes a generalized partial adjustment model of dividends in whichmanagers set target dividends based on adaptively-formed earnings prospects. Weshow that firms adjust dividends to their target payouts much faster than previ-ously documented. When managers form future earnings expectations based on alonger time-series of earnings, target dividends tend to become more stable. Thus,actual dividends tend to be more in line with the targets, driving up the speed ofadjustment. Our model offers an insight that sticky dividends could be a conse-quence of managers’ attempts to match dividend payouts with the smooth targets.

Keywords: Payout policy, Speed of adjustment, Dividend dynamics, Adaptiveexpectations

1. Introduction

Since Lintner (1956) studied corporate dividend policy and practice using apartial adjustment model, extensive prior research has documented a series of em-pirical findings and their plausible explanations.1 Yet dividends remain one of

IThe authors thank the anonymous referee, Steve Bond, and Oren Sussman for their insightfulcomments. In particular, Hyun Joong Im acknowledges Steve Bond’s valuable comments andlectures on Difference GMM and System GMM methods provided during his doctoral studies atthe University of Oxford.

∗Corresponding authorEmail addresses: cyha@phbs.pku.edu.cn (Chang Yong Ha), hyun.im@phbs.pku.edu.cn

(Hyun Joong Im), kangya@u.nus.edu (Ya Kang)1See Allen and Michaely (1995) and DeAngelo et al. (2009) for excellent reviews of the related

literature.

1

the most contested and thorniest puzzles in corporate finance (Allen et al., 2000).Research in more recent years, in particular, provides evidence that many of thoseempirical findings and underlying theories are to be revised or refuted. Amongothers, Brav et al. (2005), using survey and field interviews with financial exec-utives, provide a new perspective on various aspects of corporate payout policysuch as managers’ beliefs and stances concerning dividend policy and its deter-minants. Of particular interest for this paper is their finding that more than four-fifths of executives target to remain consistent with historical dividend policy andtake lagged dividends as a benchmark when choosing the current dividend pol-icy. Also, the majority of firms are known to tie their dividends to the sustainablefuture earnings. While these managerial tendencies are in line with dividend con-servatism, they also offer some clues on how firms and managers are likely to setthe dividend targets.

Building on the documented managerial attention to past dividend history andfuture earnings prospects in setting today’s dividend policy, this study aims tooffer a novel insight into the mechanism through which firms’ actual dividendsremain sticky.2 To that end, we propose a generalized partial adjustment modelwith adaptive expectations for future earnings.3 In our proposed model, the man-agerial attention to past dividends is reflected in the way managers form the futureearnings prospects which has also been documented to be an important consid-eration for dividend payout decision. Hence, our model does capture the spiritof managers’ tendency to consider both historical dividends and future earningsprospects in determining the current dividend policy. Our model is also consis-tent with managers’ motive to maintain smooth dividends because of asymmetricresponse of the market to dividend increases and cuts. By allowing managers toset target dividends based on expected future earnings,4 our model can generate

2In Appendix A, we present the analysis of the time-series evolution of dividends for ourcross-section of the firms following Lemmon et al. (2008). A preliminary examination revealsthe presence of a permanent or long-run component that leads to highly persistent cross-sectionaldifferences in dividend ratios. In addition, both nonparametric and parametric (ANCOVA) analy-ses of variance decomposition show that the time-invariant firm-specific components are the majorsource of total variation in dividends. That is, the majority of the total variation in dividends comesfrom cross-sectional differences as opposed to time-series variation. See Appendix A for furtherdetails.

3Chow (2011) provides a statistical reason and strong econometric evidence for supporting theadaptive expectations hypothesis in economics.

4Setting dividend targets in this manner is in line with the signaling hypothesis of dividends(Bhattacharya, 1979; Miller and Rock, 1985; John and Williams, 1985).

2

a smoother path of target dividends provided that managers form expectationsadaptively when assessing future earnings prospects. Note that with adaptive ex-pectation formation, future earnings prospects are formed as a weighted averageof current and past earnings with geometrically declining weights.

Among the reported stylized facts lie the slow adjustments of dividends to-ward target payouts. For example, Fama and Babiak (1968) and Fama and French(2002) report quite low adjustment speeds of 0.37 and 0.33, respectively. Giventhe volatility in firms’ earnings, it has remained a puzzle that actual dividendspaid out do not reflect that volatility. Our model allows us to reexamine the ad-justment speed of dividends to payout targets by explicitly modeling the dividendtarget formation process. Existing research often attributes smooth dividends tofirms’ reluctance to change dividends due to asymmetric information (i.e., signal-ing effect (Bhattacharya, 1979)) or agency conflicts (e.g., irrelevance of short-termprofits to dividend decision (Easterbrook, 1984)).5 One important implication ofthose theories is that the manager’s information set for dividend decision is likelyto contain a longer series of past dividends as well as future earnings prospects.Incorporating this aspect of firms’ dividend decisions, this study provides an al-ternative and richer explanation for this long-lived puzzle by showing that firms’target dividend payouts themselves are much “smoother” than previously docu-mented. While volatile target payouts in conventional models result in fairly lowspeeds of adjustment, our estimation results suggest that firms tend to adjust theirdividend payouts to the targets much faster.

2. Data and methodology

This study uses annual accounting data from the CRSP/Compustat MergedDatabase (CCM) for the years 1970–2015. Firms with standard industrial classi-fication (SIC) codes between 6000 and 6999, between 4900 and 4999, or between9000 and 9999 are excluded as these firms are in financial services, regulated util-ities, or public administration. We require that each firm have at least 12 years ofobservations and there be no gaps in the middle of the sample period. We drop theobservations if the dividend-to-total assets ratio (denoted Di,t), earnings-to-totalassets ratio (denoted Ei,t), or a proxy for Tobin’s Q as measured by the sum of thebook value of debt and market value of equity divided by the book value of totalassets (denoted Qi,t) is missing. All variables are winsorized at the 1st and 99th

5See Leary and Michaely (2011) for a comprehensive survey of the theoretical models.

3

percentiles to minimize the effects of outliers. There are a total of 24,926 firm-year observations, corresponding to 981 firms. Industry dummies are constructedaccording to Fama and French’s (1997) 48 industry classification.

Waud (1966) shows that a conventional partial adjustment model and an adap-tive expectations model yield indistinguishable empirical specifications as far asestimation is concerned. Hence, one cannot tell whether the estimated coefficientof the lagged dividend ratio is driven by the speed of dividend adjustment (γ) orthe speed of expectations revision (ρ). See Appendix B for a detailed discussionof the identification problem. A novel feature of our model presented in this sec-tion is that it includes the ingredients of both the partial adjustment model andthe adaptive expectations model. This feature allows us to sort out the respectiveeffects of dividend adjustment speed (γ) and expectations revision speed (ρ) in thedynamics of corporate dividend policy. In addition, our model takes into accountunobserved firm heterogeneity in setting dividend targets.

A generalized partial adjustment model of dividends with an adaptive expec-tations formation process in the panel data setting consists of the following threeequations:

Di,t −Di,t−1 = γ(D?i,t −Di,t−1)+π j +κt +νi,t ; (1)

D?i,t = αEe

i,t +βQi,t−1 +µi; (2)Ee

i,t −Eei,t−1 = ρ(Ei,t −Ee

i,t−1), (3)

where 0 < γ ≤ 1 and 0 < ρ ≤ 1.6 Equation (1) describes the partial adjustment

6An alternative way to separately identify the dividend adjustment speed (γ) and the expec-tations revision speed (ρ) would be to estimate firm-specific time-series regressions and averagefirm-specific estimates for the two speeds. The firm-specific model can be written as follows:

Dt −Dt−1 = γ(D?t −Dt−1)+νt ;

D?t = αEe

t +βQt−1 +µ;Ee

t −Eet−1 = ρ(Et −Ee

t−1),

where 0 < γ ≤ 1 and 0 < ρ ≤ 1. Dt and D?t denote the actual and target dividends per share

(or the actual and target dividend ratios) in year t. Et denotes the earnings per share (or theearnings ratio) observed in period t, and Ee

t−1 and Eet denote the earnings per share (or the earnings

ratios) expected to prevail in periods t −1 and t, respectively. One can estimate the reduced-formfirm-specific time-series regression model similar to Equation (7) firm by firm and aggregate theestimates of firm-specific parameters. However, this method is not feasible when annual datais used. In our sample, the median number of complete time-series observations for each firmis only 21. See Figure 1 for the histogram and kernel density curve for the distribution of the

4

process of dividends. Di,t and D?i,t denote the actual and target dividend ratios of

firm i in year t. γ in Equation (1) denotes the speed of adjustment which measureshow fast firms adjust to their target or optimal dividends. The error term in thepartial adjustment equation consists of three parts. π j and κt represent unobservedindustry-specific and year-specific effects, and νi,t represents the idiosyncratic er-ror with zero mean and no serial correlation. Note that the error components π jand κt can be replaced by industry dummies and year dummies, respectively.

Equation (2) describes how the target dividend ratio is determined. We modifythe conventional partial adjustment model described in Appendix B so that the tar-get dividend ratio is determined by adaptively-formed earnings expectations ratherthan statically-formed earnings expectations. To make γ and ρ separately identifi-able, we also include Tobin’s Q measured at the beginning of year t (Qi,t−1) as anadditional observable determinant of the target payout ratio. In addition, we allowthe target dividend ratio to be affected by unobserved firm-specific effects (µi).Lintner (1956), Fama and Babiak (1968), and Fama and French (2002) model thetarget dividend ratio as a function of observed current earnings, but do not includeunobserved firm-specific effects. In the second equation, α and β capture targetdividends–expected earnings sensitivity and target dividends–Tobin’s Q sensitiv-ity, respectively.

Most of classical literature directly related to the estimation of the partialadjustment model of dividends (e.g., Lintner (1956), Fama and Babiak (1968),Dewenter and Warther (1998), Skinner (2008), and Leary and Michaely (2011))simply model the target payout ratio as a function of profitability (i.e., earnings)only. However, Fama and French (2002) who jointly study the dynamics of debtand dividends model the target dividend ratio as a function of several variablessuch as future growth opportunities (i.e., Tobin’s Q), profitability (i.e., earnings),target leverage, R&D intensity, R&D dummy, and firm size. Given that mostof the literature model the target dividend ratio as a function of earnings only,

number of complete time-series observations for each firm. Not all of the coefficient estimatesare statistically significant in most of the firm-specific regressions so we cannot make reliableinferences on the dividend adjustment speed (γ) and the expectations revision speed (ρ) based onthe firm-specific regressions. Thus, consistent with recent empirical corporate finance literatureinvolving the estimation of a partial adjustment model of leverage (Flannery and Rangan, 2006;Lemmon et al., 2008; Faulkender et al., 2012; Ha et al., 2016), we use a panel data regressionmodel with cross-sectionally comparable variables. While per-share variables such as dividendsper share are not cross-sectionally comparable, standardized variables such as dividends-to-totalassets ratio are cross-sectionally comparable.

5

Figure 1: Number of complete time-series observations for each firm

050

100

150

200

Fre

quen

cy o

f firm

s

0 10 20 30 40Number of complete time−series observations for each firm

Note: This figure presents the histogram and the kernel density curve for the number of completetime-series observations for each firm. An observation is regarded as being incomplete if anyof current dividend, first-lagged dividend, second-lagged dividend, first-lagged Tobin’s Q, andsecond-lagged Tobin’s Q is missing. The pink curve presents the Epanechnikov kernel densitycurve, while the light blue bar presents the frequency of firms.

6

we proceed to generalize the commonly used framework by modeling target div-idends as a function of earnings prospects and unobserved firm-specific effects(i.e., D?

i,t = αEei,t +µi), and explicitly modeling the expectations formation process

(i.e., Eet −Ee

t−1 = ρ(Et −Eet−1)). However, one cannot identify two speed param-

eters γ and ρ separately by estimating the resultant reduced-form dynamic paneldata regression model.7 Therefore, we include Tobin’s Q at the beginning of yeart (Qi,t−1) as an additional determinant of the target payout ratio to make γ and ρ

separately identifiable. When more than one additional determinants are includedin the target payout equation, algebra becomes very complicated. Therefore, wechoose an approach of adding only one most important determinant. Among sev-eral candidates, a measure of future growth opportunities such as Tobin’s Q seemsto be most appropriate since prior studies have shown that firms’ dividend payoutpolicies are affected by the growth opportunities they have (e.g. Smith and Watts(1992)).

Equation (3) describes the adaptive expectations formation process. Ei,t isthe earnings ratio observed in period t, and Ee

i,t−1 and Eei,t are the earnings ratios

expected to prevail in periods t −1 and t, respectively. ρ represents the proportionof the expectation error taken to be permanent rather than transitory. For example,if ρ = 1, then all of the error is taken to be permanent and Ee

i,t = Ei,t .8

Substituting Equation (2) into Equation (1) gives the following equation:

Di,t = (1− γ)Di,t−1 + γD?i,t +π j +κt +νi,t

= (1− γ)Di,t−1 + γαEei,t + γβQi,t−1 + γµi +π j +κt +νi,t . (4)

Evaluating Equation (4) one period back and rearranging the equation gives thefollowing equation:

Eei,t−1 =

1γα

[Di,t−1 − (1− γ)Di,t−2 − γβQi,t−2 − γµi −π j −κt−1 −νi,t−1]. (5)

7If the second equation is specified as D?i,t = αEe

i,t +µi, one can obtain the following reduced-form regression model by employing the procedures used to obtain Equation (6):

Di,t = [(1− γ)+(1−ρ)]Di,t−1 − (1− γ)(1−ρ)Di,t−2 + γραEi,t +ηi +ξi,t ,

where ηi = γρµi and ξi,t = ρπ j+[(κt +νi,t)−(1−ρ)(κt−1+νi,t−1)]. However, one cannot identifyγ and ρ separately by estimating this reduced-form model.

8A firm’s expected earnings can be expressed as a weighted average of its current and pastobserved earnings with geometrically declining weights if 0 < ρ < 1. The weight for Ei,t−k isρ(1−ρ)k for k = 0,1,2, · · · .

7

Substituting ρEi,t +(1−ρ)Eei,t−1 for Ee

i,t in Equation (4), substituting 1γα[Di,t−1 −

(1− γ)Di,t−2 − γβQi,t−2 − γµi −π j −κt−1 −νi,t−1] for Eei,t−1, and rearranging the

equation gives the following reduced-form model:

Di,t = (1− γ)Di,t−1 + γαρEi,t + γα(1−ρ)Eei,t−1 + γβQi,t−1 + γµi +π j +κt +νi,t

= [(1− γ)+(1−ρ)]Di,t−1 + γραEi,t − (1− γ)(1−ρ)Di,t−2 + γβQi,t−1

−γ(1−ρ)βQi,t−2 + γρµi +ρπ j +[(κt +νi,t)− (1−ρ)(κt−1 +νi,t−1)]. (6)

This can be rewritten as the following standard dynamic panel regression model:

Di,t = δ1Di,t−1 +δ2Ei,t +δ3Di,t−2 +δ4Qi,t−1 +δ5Qi,t−2 +ηi +ξi,t , (7)

where δ1 = (1− γ) + (1− ρ), δ2 = γρα, δ3 = −(1− γ)(1− ρ), δ4 = γβ, δ5 =−γ(1−ρ)β, ηi = γρµi, and ξi,t = ρπ j +[(κt +νi,t)− (1−ρ)(κt−1 +νi,t−1)]. Theerror term ξi,t is an MA(1) process if each of κt and νi,t is assumed to be whitenoise.9 A consistent estimator can be obtained using System GMM suggestedby Arellano and Bover (1995) and Blundell and Bond (1998). The delta methodis employed in order to estimate structural parameters (γ, ρ, α, β) as nonlinearcombinations of regression coefficients.10

3. Results

Before we present our main results, we first estimate the conventional partialadjustment models that can be viewed as a special case of our generalized model

9This does not imply that the actual residuals always follow the process implied by the speci-fication. However, in both Difference GMM and System GMM, a different error structure wouldresult in a different set of valid instruments as suggested by the Sargan-Hansen test of overidenti-fying restrictions. A less restrictive assumption such as MA(1), compared with the case of MA(0),allows for a smaller number of valid instruments.

10We use the following nonlinear combinations of coefficients to obtain the structural parame-ters. First, dividing −δ5 by δ4 gives an estimate of 1−ρ:

−δ5

δ4=

γ(1−ρ)β

γβ= (1−ρ),

and therefore ρ = 1+ δ5δ4

. Second, we can get (1− γ) using the equation for δ1:

(1− γ) = δ1 − (1−ρ) = δ1 +δ5

δ4,

and therefore γ = 1−δ1 − δ5δ4

. Finally, α = δ2γρ

and β = δ4γ

.

8

in the sense that the speed of expectations revision (ρ) is set to 1. Thus, managersin this model form future earnings prospects based only on current earnings. Ta-ble 1 reports estimation results based on three different estimation methods, i.e.,Pooled OLS, Within Groups, and System GMM estimators. Regardless of esti-mation methods, the parameter estimates, α̂ and β̂, for target payout determinantsare significantly positive at the 1% significance level. The estimated speed of ad-justment (̂γ) is comparable to the estimates reported in previous studies.11 TheSargan-Hansen tests of overidentifying restrictions do not reject the specificationsin Columns (3) and (4).12 Note, however, that because the partial adjustmentmodel and adaptive expectations model are observationally equivalent in their es-timable forms, the parameter estimate (̂γ) which we just interpreted as the speedof dividend adjustment may, in fact, represent the speed of expectations revision(ρ̂).13

In Table 2, we report the main regression results for our generalized partialadjustment model. Although the estimation results are qualitatively similar acrossthe estimation methods, our System GMM estimates reported in Columns (3) and(4) are considered better as they are known to be consistent and efficient. More-over, our models as reported in those two columns are strongly supported by theSargan-Hansen tests and Arellano-Bond second-order serial correlation tests. Sev-eral aspects of the estimates are of particular interest. First, the estimated speed ofadjustment (̂γ) is much higher than those reported in the existing literature. Notethat, regardless of estimation methods, γ̂ is also much higher than the adjustmentspeed estimated in Table 1. The results are qualitatively similar across the esti-mation methods, although γ̂ is slightly higher with OLS estimates (̂γOLS = 0.994;

11Fama and French (2002) report an estimate of about 0.30. Dewenter and Warther (1998),on the other hand, obtain a much lower average estimate of 0.055 for 313 US firms studied. Asomewhat higher speed from the Within Groups estimation in Table 1 may be driven by the short-panel bias (Nickell, 1981).

12In Columns (3) and (4), we report the set of instruments used in first-differenced equationsand level equations. Arellano and Bond’s (1991) second-order serial correlation tests suggest thatthe error term ξit is an MA(1) process. This reduces the number of lags available as instruments.

13The System GMM model reported in Column (4) is considered the best for the followingreasons. First, the estimate for the lagged dependent variable based on System GMM lies betweenOLS and Within Groups estimates which tend to be biased upwards and downwards, respectively.Second, the goodness-of-fit score for System GMM model is slightly higher than that for WithinGroups model and the same as that for OLS model. Third, p-value for the Sargan-Hansen test ofoveridentifying restrictions in Column (4) is much higher than that in Column (3). In any case,our main regression results are reported in Table 2.

9

Table 1: Estimation results for conventional partial adjustment models of dividends

(1) (2) (3) (4)ESTIMATION METHOD Pooled OLS Within Groups System GMM System GMMVARIABLES Di,t Di,t Di,t Di,t

First-lagged dividends (Di,t−1) 0.825*** 0.692*** 0.831*** 0.819***(0.011) (0.018) (0.020) (0.025)

Current earnings (Ei,t ) 0.026*** 0.024*** 0.024*** 0.028***(0.002) (0.002) (0.004) (0.006)

First-lagged Tobin’s Q (Qi,t−1) 0.001*** 0.002*** 0.001*** 0.001**(0.000) (0.000) (0.000) (0.000)

Constant 0.001 0.004*** -0.000 -0.000(0.001) (0.001) (0.001) (0.005)

Firm fixed effects No Yes Yes YesIndustry fixed effects Yes No Yes YesYear fixed effects Yes Yes Yes Yes

Number of observations 24,926 24,926 24,926 24,926Number of firms 981 981 981 981

Goodness of fit—(Corr(Di,t , D̂i,t))2 0.834 0.832 0.833 0.834

First-order serial correlation (p-value) 0.000 0.000Second-order serial correlation (p-value) 0.000 0.000Third-order serial correlation (p-value) 0.371 0.366Sargan-Hansen test (p-value) 0.110 0.873

Dividend adjustment speed (̂γ) or 0.175*** 0.308*** 0.169*** 0.181***expectations revision speed (ρ̂) (0.011) (0.018) (0.020) (0.025)

Target dividends–current earnings sensitivity (α̂) 0.147*** 0.079*** 0.142*** 0.156***(0.008) (0.006) (0.023) (0.031)

Target dividends–Tobin’s Q sensitivity (β̂) 0.008*** 0.006*** 0.005** 0.005**(0.001) (0.001) (0.002) (0.002)

Instruments for first-differenced equationsDi,t−4, · · · ,Di,t−8 Di,t−4, · · · ,Di,t−10Ei,t−4, · · · ,Ei,t−8 Ei,t−4, · · · ,Ei,t−10Qi,t−4, · · · ,Qi,t−8 Qi,t−4, · · · ,Qi,t−10

Instruments for level equations∆Di,t−3 ∆Di,t−3∆Ei,t−3 ∆Ei,t−3∆Qi,t−3 ∆Qi,t−3

Ind. dummies Ind. dummiesYear dummies Year dummies

Note: In all four columns, we report standard errors that are asymptotically robust to both heteroskedasticity and serialcorrelation. In the last two columns, we report two-step GMM coefficients and standard errors which use the finite-sample correction proposed by Windmeijer (2005). ***, **, and * indicate significance at the 1%, 5%, and 10% levels,respectively.

10

γ̂WG = 0.933; γ̂SGMM = 0.930 ∼ 0.946). This finding corroborates our intuitionthat “sticky” dividends may not be evidence that firms do not actively reassesshow much they should pay in dividends, but that they actively align their divi-dends with the “smooth” target payouts. Consequently, the actual dividends alsotend to be smooth and the adjustment speeds are, in fact, higher than previouslydocumented. Second, the speed of expectations revision (ρ̂) is much lower than1 (ρ̂OLS = 0.384; ρ̂WG = 0.509; ρ̂SGMM = 0.449 ∼ 0.459). Note that the speed isimplicitly assumed to be 1 in the conventional partial adjustment models.14 Thisresult indicates that managers consider a longer history of performances ratherthan current earnings only in setting the target payouts, offering a plausible expla-nation for dividends’ tendency to lag behind earnings (Fama and Babiak, 1968).

Coefficients for all of the variables incorporated in Equation (6) are statisti-cally significant at the 1% or 5% level. As evidenced by the significantly positiveα̂ and β̂ in Equation (2), future earnings prospects and growth opportunities havepositive influences on target dividends. We implement the analysis of covariance(ANCOVA) to further examine the relative importance of various determinantsin capturing the variation in target dividends. Table 3 shows, as predicted, thatthe total sum of squares in the generalized model (1.008) is only a small fraction(11.6%) of the conventional model counterpart (8.659), which confirms that targetdividends remain far more stable over time in the generalized model. Similarly,Figure 2 shows that the volatility of target dividends in the generalized model isfar below that in the conventional model.

The ANCOVA results reported in Panel B of Table 3 show that time-invariantfirm-specific effects are the major source of the total variation. It is interestingto note that while the total variation explained by time-varying expected earningson a stand-alone basis is 63.2% (Column (1)), its contribution (17.4% in column(5)) is smaller than that of time-invariant firm-specific effects (31.3% in Column(5)).15 Intuitively, this suggests that much of the explanatory power of existing(target) dividend determinants comes from the cross-sectional, as opposed to time-series, variation. Overall, our results provide some new evidence that firms’ targetpayout polices may not be as puzzling as previously thought. Rather, it may be

14Thus, conventional partial adjustment models impose a strong restriction on the way managersform future earnings prospects and set the target dividends.

15The ANCOVA results reported in Panel A also show that the contribution of time-varyingexpected earnings (26.9% in Column (5)) is similar to that of time-invariant firm-specific effects(26.6% in Column (5)). This suggests that the contribution of time-invariant firm-specific effectsis larger in the case of the generalized partial adjustment model (Panel B).

11

Table 2: Estimation results for generalized partial adjustment models of dividends

(1) (2) (3) (4)ESTIMATION METHOD Pooled OLS Within Groups System GMM System GMMVARIABLES Di,t Di,t Di,t Di,t

First-lagged dividends (Di,t−1) 0.622*** 0.558*** 0.605*** 0.611***(0.023) (0.025) (0.049) (0.043)

Current earnings (Ei,t ) 0.026*** 0.025*** 0.027*** 0.029***(0.002) (0.002) (0.004) (0.004)

Second-lagged dividends (Di,t−2) 0.234*** 0.183*** 0.235*** 0.222***(0.020) (0.019) (0.043) (0.038)

First-lagged Tobin’s Q (Qi,t−1) 0.003*** 0.003*** 0.002*** 0.002***(0.000) (0.000) (0.001) (0.001)

Second-lagged Tobin’s Q (Qi,t−2) -0.002*** -0.001*** -0.001** -0.001**(0.000) (0.000) (0.000) (0.000)

Constant 0.001 0.003*** 0.002* -0.001(0.001) (0.001) (0.001) (0.001)

Firm fixed effects No Yes Yes YesIndustry fixed effects Yes No Yes YesYear fixed effects Yes Yes Yes Yes

Number of observations 23,653 23,653 23,653 23,653Number of firms 979 979 979 979

Goodness of fit—(Corr(Di,t , D̂i,t))2 0.840 0.838 0.840 0.840

First-order serial correlation (p-value) 0.000 0.000Second-order serial correlation (p-value) 0.152 0.184Sargan-Hansen test (p-value) 0.096 0.868

Dividend adjustment speed (̂γ) 0.994*** 0.933*** 0.946*** 0.930***(0.052) (0.064) (0.135) (0.125)

Expectations revision speed (ρ̂) 0.384*** 0.509*** 0.449** 0.459***(0.053) (0.067) (0.132) (0.123)

Target dividends–expected earnings sensitivity (α̂) 0.067*** 0.053*** 0.063** 0.069***(0.007) (0.005) (0.014) (0.014)

Target dividends–Tobin’s Q sensitivity (β̂) 0.003*** 0.003*** 0.002** 0.002***(0.000) (0.000) (0.001) (0.001)

Instruments for first-differenced equationsDi,t−4, · · · ,Di,t−8 Di,t−4, · · · ,Di,t−10Ei,t−4, · · · ,Ei,t−8 Ei,t−4, · · · ,Ei,t−10Qi,t−4, · · · ,Qi,t−8 Qi,t−4, · · · ,Qi,t−10

Instruments for level equations∆Di,t−3 ∆Di,t−3∆Ei,t−3 ∆Ei,t−3∆Qi,t−3 ∆Qi,t−3

Ind. dummies Ind. dummiesYear dummies Year dummies

Note: In all four columns, we report standard errors that are asymptotically robust to both heteroskedasticity and serialcorrelation. In the last two columns, we report two-step GMM coefficients and standard errors which use the finite-sample correction proposed by Windmeijer (2005). ***, **, and * indicate significance at the 1%, 5%, and 10% levels,respectively.

12

Figure 2: Comparison of volatilities of target dividends: conventional vs. generalized models

0.0

05.0

1.0

15.0

2.0

25.0

3V

olat

ility

of t

arge

t div

iden

ds in

the

gene

raliz

ed m

odel

0 .005 .01 .015 .02 .025 .03Volatility of target dividends in the conventional model

Firm 45 degree line

Note: This figure plots within-firm volatilities of target dividends in the generalized model againstthose in the conventional model. Each circle represents a firm among 969 firms.

13

the case that managers set target payouts cautiously by conditioning them on alonger stretch of available earnings data. The smooth dividend paths observed inthe market, therefore, may be rational responses to target payouts determined insuch a way, resulting in higher speeds of adjustment to the targets.

4. Conclusion

This study proposes a generalized partial adjustment model of dividends inwhich managers form future earnings prospects adaptively and set the target div-idends based on the earnings prospects. The main contribution of this study is topresent new evidence with respect to the dynamic behavior of firms’ dividend poli-cies. We show that the slow adjustments of dividends to target payouts reportedusing conventional models largely stem from a strong restriction imposed on theway firms determine their dividend targets. Given that firms’ earnings are quitevolatile, the target payouts themselves will be more volatile when managers setthe targets solely based on the current earnings compared to when they use adap-tive expectations. This will, in turn, lead to larger deviations of actual dividendpayouts from the targets and hence slower speeds of dividend adjustments, ceterisparibus, making it more challenging to account for firms’ dividend payout poli-cies. If target dividends set by managers are smoother, on the other hand, actualdividends observed in the market will become more in line with the targets, driv-ing up the speed of adjustment. Our model offers an insight that smooth dividendpaths could be a consequence of managers’ attempts to match dividend payoutswith the targets. A variance decomposition analysis shows that firm-specific ef-fects are predominant sources of variations in target payouts, suggesting that themajority of the total variation in target dividends is due to time-invariant factors.

Appendix

A. Empirical evidence for sticky dividends

We begin our analysis by studying the evolution of dividend ratios for ourcross-section of firms in the spirit of Lemmon et al. (2008). Figure A.1 presentsthe average dividend-to-total assets ratios of three actual portfolios in “event time.”The figure is constructed in the following manner. Each calendar year, we sortfirms into three portfolios based on their dividend ratios, which we denote: Above

14

Table 3: Variance decompositions of target dividends

Panel A. Target dividends from the conventional partial adjustment model

(1) (2) (3) (4) (5)VARIABLES D?

i,t D?i,t D?

i,t D?i,t D?

i,t

Current earnings (Ei,t ) 0.669 0.420 0.269Tobin’s Q (Qi,t−1) 0.314 0.065 0.020Firm-specific effects (µi) 0.642 0.266

Number of Observations 24,926 24,926 24,926 24,926 24,926Root MSE 0.011 0.015 0.010 0.011 0.000Adjusted R-Squared 0.669 0.314 0.735 0.627 1.000

Total Sum of Squares 8.659

Panel B. Target dividends from the generalized partial adjustment model

(1) (2) (3) (4) (5)VARIABLES D?

i,t D?i,t D?

i,t D?i,t D?

i,t

Expected earnings (Eei,t ) 0.632 0.345 0.174

Tobin’s Q (Qi,t−1) 0.342 0.056 0.018Firm-specific effects (µi) 0.741 0.313

Number of observations 21,222 21,222 21,222 21,222 21,222Root MSE 0.004 0.006 0.004 0.004 0.000Adjusted R-Squared 0.632 0.342 0.688 0.728 1.000

Total Sum of Squares 1.008

Note: We compute the partial sum of squares for each effect in the model and then normalize each estimate by the totalsum of squares. For example, in Column (5) of Panel B, 31.3% of the total sum of squares can be attributed to unobservedfirm-specific effects (µi). Expected earnings are computed as follows: Ee

i,t = ∑4k=0(1− ρ̂)kρ̂Ei,t−k where ρ̂ is the estimated

speed of expectation revision reported in Column (4), Table 2. To compute fixed effects in target dividends, we go throughthe following procedures. First, we compute within-firm average residuals in the dynamic regression model. Second, weadd the mean of time effects to the within-firm average residuals to get firm-specific effects in dividends (ηi). Finally,we divide the firm-specific effects in dividends by γ̂ (̂γρ̂) to estimate firm-specific effects in target dividends (µi) in theconventional (generalized) model.

15

median, Below median, and Zero dividend.16 The portfolio formation year isdenoted event year 0. We then compute the average dividend for each portfolio ineach of the subsequent 20 years, holding the portfolio composition constant (butfor firms that exit the sample). We repeat these two steps of sorting and averagingfor every year in the sample period. This process generates 25 sets of event-time averages, one for each calendar year in our sample.17 We then calculatethe averages of the average dividend-to-total assets ratios across the 25 sets withineach event year, which are shown in bold lines. Surrounding dotted lines represent95% confidence intervals.

Several features of the figure are noteworthy. First, there exist a great deal ofcross-sectional differences in the average dividend-to-total assets ratios in the ini-tial portfolio formation period. Average dividend of the above-median-dividendportfolio is 5.3%, while average dividend of the below-median-dividend portfoliois only 0.9% and average dividend of the zero-dividend portfolio is exactly 0.0%.Second, there is significant divergence among all three portfolio averages over theevent time. After 20 years, the above-median-dividend portfolio has increasedto 15.7%, whereas the below-median-dividend portfolio (the zero-dividend port-folio) has increased to 1.2% (1.0%). Note that the average dividends across theportfolios 20 years later remain significantly different, both statistically and eco-nomically. When compared to the cross-sectional average of within-firm standarddeviation of dividend-to-total assets ratios (1.3%), this differential is economi-cally huge. Therefore, a preliminary examination of dividend ratios suggests thepresence of a permanent or long-run component that leads to highly persistentcross-sectional differences in dividend ratios.

We then move on to a variance decomposition of dividend-to-total assets ra-tios. We begin with a nonparametric framework. Specifically, we compute thewithin- and between-firm variations of dividend ratios, finding that these esti-mates in terms of standard deviation are 1.23% and 1.59%, respectively. Thus,the between-firm variation is approximately 29% larger than the within-firm varia-tion. Intuitively, this suggests that dividend varies significantly more across firms,as opposed to within firms over time, consistently with the patterns observed in

16The median is calculated using the sample consisting of firms with positive dividends in theportfolio formation year.

17As we require that firms exist for at least 20 years after the formation of portfolios, we performthe portfolio formation each year from 1971 to 1995 for our sample. We start from 1971 as welose one observation due to the use of lagged total assets when we compute the dividend-to-totalassets ratio.

16

Figure A.1: Average dividend-to-total assets ratios of actual dividend portfolios in event time

0.0

2.0

4.0

6.0

8.1

.12

.14

.16

Div

iden

d−to

−to

tal a

sset

s ra

tio

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Event time

Zero dividend Below median Above median

Note: This figure plots average dividend-to-total assets ratios of actual dividend portfolios. Thesample consists of all firms (excluding financial firms, regulated utilities, or government entities)from the CCM database from 1970 to 2015. To obtain this figure, first, for each calendar yearfrom 1971 to 1995, we sort the firms into three groups based on dividend-to-total assets ratios(denoted as Zero dividend, Below median, and Above median) and calculate the average ratios foreach of the three portfolios in each of the subsequent 20 years, holding the portfolio compositionconstant. We use the median based on the sample consisting of firms with positive dividends inthe portfolio formation year. We repeat this process for all the years from 1971 to 1995. Thisprocess generates 25 sets of event-time averages. Second, we compute the average of the averagedividend-to-total assets ratios across the 25 sets within each event year to obtain the bold lines inthe figure. Surrounding dotted lines represent 95% confidence intervals.

17

Table A.1: Variance decompositions of actual dividends

(1) (2) (3) (4) (5)VARIABLES Di,t Di,t Di,t Di,t Di,t

Current earnings (Ei,t ) 0.229 0.100 0.022Tobin’s Q (Qi,t−1) 0.225 0.095 0.012Firm-specific effects (ηi) 0.637 0.360

Number of Observations 25,110 25,110 25,110 25,110 25,110Root MSE 0.018 0.018 0.017 0.012 0.012Adjusted R-Squared 0.229 0.225 0.324 0.623 0.671

Total Sum of Squares 10.392

Note: We compute the partial sum of squares for each effect in the model and then normalize each estimate by the total sumof squares. For example, in Column (5), 36.0% of the total sum of squares can be attributed to unobserved firm-specificeffects (ηi).

Figure A.1. We now turn to a parametric framework, analysis of covariance (AN-COVA), to decompose the variation in actual dividends attributable to differentfactors. Table A.1 shows that firm-specific effects (ηi) account for 36.0% of thetotal sum of squares (10.392) in the specification reported in Column (5). This alsosuggests that the time-invariant firm-specific components are the major source oftotal variation in dividends.

B. An identification problem

In this section we show that a conventional partial adjustment model and anadaptive expectations model yield indistinguishable empirical specifications forthe dividend adjustment process.18 Nesting both models as special cases, ourproposed model allows partial adjustment behavior and expectation updating towork together to characterize firms’ dynamic dividend adjustment behavior. Theconventional partial adjustment models of dividends found in the literature can bespecified as the following three equations:

Di,t −Di,t−1 = γ(D?i,t −Di,t−1)+π j +κt +νi,t ; (B.1)

D?i,t = αEe

i,t +µi; (B.2)Ee

i,t = Ei,t , (B.3)

18Although their proof is not done in the panel data setting, Waud (1966) first shows that aconventional partial adjustment model and an adaptive expectations model yield indistinguishableempirical specifications as far as estimation is concerned.

18

where Di,t and D?i,t denote the actual and target dividends (scaled by assets) of firm

i in year t.19 The target dividend ratio, D?i,t , is determined by statically-formed

earnings expectations (Eei,t) and unobserved firm-specific effects (µi). Note that

the conventional partial adjustment model implicitly assumes that earnings ex-pectations are formed statically, i.e., Ee

i,t = Ei,t (Waud, 1966).20 Thus, the targetdividend ratio is essentially determined by a fraction (α) of observed current earn-ings (scaled by assets) (Ei,t) and unobserved firm-specific effects (µi), where α

denotes the target payout ratio to be applied to current earnings.21 γ representsthe speed of adjustment which measures how fast firms adjust to their target oroptimal dividends.

With some substitutions and re-parameterizations, we finally obtain the fol-lowing standard dynamic panel regression model:

Di,t = b1Di,t−1 +b2Ei,t +ηi +ξi,t , (B.4)

for i = 1, · · · ,N and t = 2, · · · ,T where b1 = (1− γ) and b2 = γα. Therefore, thespeed of adjustment can be estimated as γ̂ = 1− b̂1. Similarly, the sensitivity oftarget dividends to earnings can be estimated as α̂ = b̂2/(1− b̂1).

We now consider an adaptive expectations model of dividends to highlight amajor potential cause of the reported slow dividend adjustment speeds. It mayarise from the fact that the dynamic panel regression models used to estimatethe adjustment speed can also be derived by assuming that firms adaptively formexpectations of their earnings to determine their actual dividend policies. Theexpectation formation process is specified as follows:

Eei,t −Ee

i,t−1 = ρ(Ei,t −Eei,t−1), (B.5)

where 0 < ρ ≤ 1. Ei,t is the earnings ratio observed in period t, and Eei,t−1 and Ee

i,tare the earnings ratios expected to prevail in periods t − 1 and t, respectively. ρ

19The error term in the partial adjustment equation consists of three parts. π j and κt representunobserved industry-specific and year-specific effects, and νi,t represents the idiosyncratic errorwith zero mean and no serial correlation. Note that the error components π j and κt can be replacedby industry dummies and year dummies, respectively.

20The static expectations formation is essentially a special case of the adaptive expectations for-mation in that the static expectations formation process is equivalent to the adaptive expectationsformation process with ρ = 1.

21Lintner (1956), Fama and Babiak (1968), and Fama and French (2002) also model the targetdividend ratio as a function of observed current earnings, but do not include unobserved firm-specific effects.

19

represents the proportion of the expectation error (Ei,t −Eei,t−1) taken to be per-

manent rather than transitory. For example, if ρ = 1, then all of the error is takento be permanent and Ee

i,t = Ei,t . Note that a firm’s expected earnings can be ex-pressed as a weighted average of its current and past observed earnings with geo-metrically declining weights if 0 < ρ < 1. The weight for Ei,t−k is ρ(1−ρ)k fork = 0,1,2, · · · .

Assume now that the expected earnings ratio (Eei,t) determines the actual divi-

dend ratio Di,t :Di,t = αEe

i,t +µi +π j +κt +νi,t . (B.6)

Substituting ρEi,t +(1−ρ)Eei,t−1 for Ee

i,t , substituting 1α(Di,t−1 −µi −π j −κt−1 −

νi,t−1) for Eei,t−1, and rearranging the equation gives the following standard dy-

namic panel regression model:

Di,t = b1Di,t−1 +b2Ei,t +ηi +ξi,t , (B.7)

for i = 1, · · · ,N and t = 1, · · · ,T where b1 = (1−ρ) and b2 = ρα. Therefore, thespeed of expectations revision can be estimated as ρ̂ = 1− b̂1.

It can clearly be seen that the reduced-form equations for the partial adjust-ment model and the adaptive expectations model are indistinguishable. Hence,one cannot tell whether the estimated coefficient of the lagged dividend ratio (b̂1)is driven by the speed of dividend adjustment (γ) or the speed of expectations revi-sion (ρ). That is, one cannot separately identify γ and ρ using the dynamic paneldata regression model described above. Therefore, we use a generalized partialadjustment model with an adaptive expectations formation process which rendersboth parameters identifiable. The model is described in Section 2.

20

Allen, F., Bernardo, A. E., Welch, I., 2000. A theory of dividends based on taxclienteles. Journal of Finance 55 (6), 2499–2536.

Allen, F., Michaely, R., 1995. Dividend policy. Handbooks in Operations Re-search & Management Science 9, 793–837.

Arellano, M., Bond, S., 1991. Some tests of specification for panel data: Montecarlo evidence and an application to employment equations. Review of Eco-nomic Studies 58 (2), 277–297.

Arellano, M., Bover, O., 1995. Another look at the instrumental variable estima-tion of error-components models. Journal of Econometrics 68 (1), 29–51.

Bhattacharya, S., 1979. Imperfect information, dividend policy, and “the bird inthe hand” fallacy. Bell Journal of Economics 10 (1), 259–270.

Blundell, R., Bond, S., 1998. Initial conditions and moment restrictions in dy-namic panel data models. Journal of Econometrics 87 (1), 115–143.

Brav, A., Graham, J. R., Harvey, C. R., Michaely, R., 2005. Payout policy in the21st century. Journal of Financial Economics 77 (3), 483–527.

Chow, G. C., 2011. Usefulness of adaptive and rational expectations in economics,Princeton University CES Working Paper No. 221.

DeAngelo, H., DeAngelo, L., Skinner, D. J., et al., 2009. Corporate payout policy.Foundations and Trends in Finance 3 (2–3), 95–287.

Dewenter, K. L., Warther, V. A., 1998. Dividends, asymmetric information, andagency conflicts: Evidence from a comparison of the dividend policies ofJapanese and US firms. Journal of Finance 53 (3), 879–904.

Easterbrook, F. H., 1984. Two agency-cost explanations of dividends. AmericanEconomic Review 74 (4), 650–659.

Fama, E. F., Babiak, H., 1968. Dividend policy: An empirical analysis. Journal ofthe American Statistical Association 63 (324), 1132–1161.

Fama, E. F., French, K. R., 1997. Industry costs of equity. Journal of FinancialEconomics 43 (2), 153–193.

21

Fama, E. F., French, K. R., 2002. Testing trade-off and pecking order predictionsabout dividends and debt. Review of Financial Studies 15 (1), 1–33.

Faulkender, M., Flannery, M. J., Hankins, K. W., Smith, J. M., 2012. Cash flowsand leverage adjustments. Journal of Financial Economics 103 (3), 632–646.

Flannery, M. J., Rangan, K. P., 2006. Partial adjustment toward target capital struc-tures. Journal of Financial Economics 79 (3), 469–506.

Ha, C. Y., Im, H. J., Kang, Y., Shon, J., 2016. Uncertainty, major investments, andcapital structure dynamics, Peking University HSBC Business School WorkingPaper No. 2016003.

John, K., Williams, J., 1985. Dividends, dilution, and taxes: A signalling equilib-rium. Journal of Finance 40 (4), 1053–1070.

Leary, M. T., Michaely, R., 2011. Determinants of dividend smoothing: Empiricalevidence. Review of Financial Studies 24 (10), 3197–3249.

Lemmon, M. L., Roberts, M. R., Zender, J. F., 2008. Back to the beginning: per-sistence and the cross-section of corporate capital structure. Journal of Finance63 (4), 1575–1608.

Lintner, J., 1956. Distribution of incomes of corporations among dividends, re-tained earnings, and taxes. American Economic Review 46 (2), 97–113.

Miller, M. H., Rock, K., 1985. Dividend policy under asymmetric information.Journal of Finance 40 (4), 1031–1051.

Nickell, S., 1981. Biases in dynamic models with fixed effects. Econometrica,1417–1426.

Skinner, D. J., 2008. The evolving relation between earnings, dividends, and stockrepurchases. Journal of Financial Economics 87 (3), 582–609.

Smith, C. W., Watts, R. L., 1992. The investment opportunity set and corporate fi-nancing, dividend, and compensation policies. Journal of Financial Economics32 (3), 263–292.

Waud, R. N., 1966. Small sample bias due to misspecification in the “partial ad-justment” and “adaptive expectations” models. Journal of the American Statis-tical Association 61 (316), 1130–1152.

22

Windmeijer, F., 2005. A finite sample correction for the variance of linear efficienttwo-step GMM estimators. Journal of Econometrics 126 (1), 25–51.

23